Robust LQG optimal controller synthesis against noise spectral uncertainties and nonlinear time-varying unmodeled dynamics

Abstract

In this paper, we consider the problem of robust controller synthesis against noise spectral uncertainties and nonlinear time-varying (NLTV) unmodeled dynamics in the discrete LQG (linear-quadratic Gaussian) optimal systems. We derive a necessary and sufficient condition for robust stabilization in multivariable stochastic discrete-time systems with NLTV unmodeled dynamics. Meanwhile, an algorithm based on the robust stabilization criterion is presented for synthesizing a robust controller not only to minimize the least favorable cost functional J but also to satisfy the robust stabilization criterion by specifying an appropriate weighting scalar in the cost functional.